In this data exploration we are looking at the US Real Estate market with use of a dataset from kaggle published by Ahmed Shahriar Sakib. It contains over 2.2 Million Real Estate listings broken down to State, Size, Price (among other factors). (Source: https://www.kaggle.com/datasets/ahmedshahriarsakib/usa-real-estate-dataset/data)
Data import
data =read.csv("data/realtor-data.zip.csv") # Data import
Data Transformation
data =subset(data, select =c(status, price, bed, bath, acre_lot, city, state, house_size)) # keep relevant columns
Structure with standard datatypes
Code
structure_tbl <- tibble::tibble(Variable =names(data),Type =sapply(data, function(x) class(x)[1]),Example =sapply(data, function(x) { val <-unique(x[!is.na(x)])[1]if (is.factor(val)) as.character(val) }),Missing =sapply(data, function(x) sum(is.na(x))))kable( structure_tbl,caption ="Structure summary of the dataset",align =c("l", "l", "l", "r"))
Structure of cleaned dataset
Variable
Type
Example
Missing
status
character
NULL
0
price
numeric
NULL
1541
bed
integer
NULL
481317
bath
integer
NULL
511771
acre_lot
numeric
NULL
325589
city
character
NULL
0
state
character
NULL
0
house_size
numeric
NULL
568484
Code
# Assign Data Typesdata$status =as.factor(data$status)data$city =as.factor(data$city)data$state =as.factor(data$state)
NA Removal
Code
before_rows <-nrow(data)data <-na.omit(data)after_rows <-nrow(data)kable(data.frame(Description =c("Before NA removal", "After NA removal"),Rows =c(before_rows, after_rows)))
Description
Rows
Before NA removal
2226382
After NA removal
1360716
The dataset now has 1360716 observations and 8 variables after removing rows with missing values.
Filtering
Code
# Filter min and max valuesdata = data |>filter(price >10000& price <1000000000)
Calculations
Code
data = data |>mutate(price_per_sqm = price/house_size)
Cleaned Dataset
Code
paged_table(data)
Structure after transformation
Code
structure_tbl <- tibble::tibble(Variable =names(data),Type =sapply(data, function(x) class(x)[1]),Example =sapply(data, function(x) { val <-unique(x[!is.na(x)])[1]if (is.factor(val)) as.character(val) elseas.character(round(val, 2)) }),Missing =sapply(data, function(x) sum(is.na(x))))kable( structure_tbl,caption ="Structure summary of the dataset",align =c("l", "l", "l", "r"))
Structure of cleaned dataset
Variable
Type
Example
Missing
status
factor
for_sale
0
price
numeric
105000
0
bed
integer
3
0
bath
integer
2
0
acre_lot
numeric
0.12
0
city
factor
Adjuntas
0
state
factor
Puerto Rico
0
house_size
numeric
920
0
price_per_sqm
numeric
114.13
0
After cleaning the dataset, all variables have appropriate data types and no missing values (n = 1360076):
status – Factor variable showing the listing status (e.g., for_sale, sold).
price – Numeric value for the property’s price in USD.
bed, bath – Integer counts of bedrooms and bathrooms.
acre_lot – Numeric size of the lot (in acres).
city, state – Factor variables identifying the property’s location.
house_size – Numeric size of the house (in square feet).
price_per_sqm – Numeric variable derived from price / house_size to compare prices across properties.
All rows with missing data were removed, and categorical variables were converted to factors for easier analysis and visualization later on.
Data dictionary
Code
tibble(Variable =c("price", "status", "acre_lot", "state", "house_size"),Description =c("The price for which the item was listed on the market","The status if the house is already sold or still for sale","The size of the land / lot on which the house is located in acres","The state in which the house is located","The size of the house in square feet" )) |>kable(caption ="Description of key variables in the dataset",align =c("l", "l") )
Description of key variables in the dataset
Variable
Description
price
The price for which the item was listed on the market
status
The status if the house is already sold or still for sale
acre_lot
The size of the land / lot on which the house is located in acres
state
The state in which the house is located
house_size
The size of the house in square feet
Summary statistic tables
In this section we will cover the summary of our cleaned dataset. We will explore basic statistical values from our data.
Top categories for factor variables with counts, proportions, and mean price
Variable
Category
Count
Percent
Mean_Price
city
Houston
19226
1.41
477651
city
Tucson
7876
0.58
384816
city
Phoenix
7694
0.57
543665
city
Los Angeles
7556
0.56
1885626
city
Dallas
7510
0.55
587276
city
Philadelphia
7336
0.54
338467
city
Richmond
6592
0.48
392538
city
Orlando
6281
0.46
418841
city
Fort Worth
6171
0.45
389780
city
Saint Louis
5970
0.44
250029
state
California
170954
12.57
1095518
state
Texas
145394
10.69
451253
state
Florida
127675
9.39
649826
state
Arizona
54488
4.01
552916
state
Pennsylvania
51922
3.82
343792
state
New York
50935
3.75
669257
state
Georgia
49234
3.62
422988
state
Illinois
46901
3.45
357316
state
Washington
46450
3.42
728113
state
Virginia
44236
3.25
547994
status
for_sale
750493
55.18
621383
status
sold
609583
44.82
515063
Interpretation
city: Most listings in Houston, Tucson, Phoenix, and Los Angeles. Prices range widely — highest in Los Angeles (~$1.9M), lowest around $250k (Saint Louis).
state: California, Texas, and Florida dominate listings (>30% total). California shows the highest mean price (~$1.1M).
status: 55% for sale, 45% sold. Active listings are priced higher (~$621k vs. $515k).
Overall: Listings cluster in major U.S. cities and states, with strong regional price differences, especially high in California and large metro areas.
Visualisation of nominal variables (top categories)
Code
nominal_summary <- nominal_summary |>group_by(Variable) |>mutate(Category = forcats::fct_reorder(Category, Count),Category =factor(Category, levels =unique(Category))) |>ungroup()# Plot: Facets untereinander, mit eigener x-Skala und y-Skala pro Variableggplot(nominal_summary, aes(x = Count, y = Category, fill = Variable)) +geom_col(show.legend =FALSE, alpha =0.8, width =0.7) +facet_wrap(~ Variable, ncol =1, scales ="free", drop =TRUE) +scale_x_continuous(labels =label_comma()) +#Tausendertrennung, keine 1e+05theme_minimal() +labs(title ="Top Categories per Factor Variable",x ="Count",y ="Category" ) +theme(panel.spacing.y =unit(1, "lines"),strip.text =element_text(size =12, face ="bold"),axis.text.y =element_text(size =8),plot.margin =margin(5, 15, 5, 5) )
# Stichprobe ziehen für Performanceset.seed(123)sample_data <- data %>%sample_n(50000)plot_ly( sample_data,x =~house_size,y =~price,color =~status,type ="scatter",mode ="markers",alpha =0.6) %>% plotly::layout(title =list(text ="Relationship Between House Size and Price by Status"),xaxis =list(title ="House Size (sqft)"),yaxis =list(title ="Price ($)", type ="log") )
Interpretation
Positive relationship: Larger houses generally have higher prices, though the relationship weakens for very large properties.
Status comparison: Both for_sale and sold homes follow similar trends, but for_sale listings appear higher in price, suggesting sellers may list above sale values.
High variation: At similar sizes, prices vary widely — showing the strong influence of location and other factors.
Outliers: A few extremely large or expensive properties stretch the scale upward.
Multiple Regression
Code
model <-lm(price ~ house_size + bath + bed + state + status, data = data)tidy(model) |>arrange(p.value) |>mutate(estimate =round(estimate, 1),std.error =round(std.error, 1),statistic =round(statistic, 1),p.value =signif(p.value, 3) ) |>datatable(caption ="Regressionsergebnisse (interaktiv)",filter ="top", options =list(pageLength =10, autoWidth =TRUE,responsive =TRUE ) )
Regional variation: Western and coastal states show generally higher property prices, while central regions are lower.
Highest averages: States like California, New York, and Washington stand out with mean prices well above $1M.
Moderate prices: States such as Texas, Florida, and Arizona fall in the mid-range (~$400–650K).
Lower averages: Midwest and Southern states have more affordable properties on average.
Summary: Property values are heavily influenced by geography — with the highest prices concentrated along the coasts and major urban centers.
Average House Size Map
Code
map_size <- data %>%group_by(state) %>%summarise(avg_size =mean(house_size, na.rm =TRUE), .groups ="drop") %>%inner_join(valid_states, by =c("state"="state_name"))plot_ly( map_size,type ="choropleth",locationmode ="USA-states",locations =~state_abbr,z =~avg_size,text =~paste0(state, "<br>Avg Size: ", round(avg_size), " sqft"),colorscale ="Greens",colorbar =list(title ="Avg Size (sqft)")) %>% plotly::layout(title =list(text ="Average House Size by U.S. State"),geo =list(scope ="usa", projection =list(type ="albers usa")) )
Interpretation
General trend: Average house sizes are fairly consistent across most states, typically around 2,000–2,500 sqft.
Larger homes: Some central and mountain states (e.g., Colorado, Utah, Iowa) show slightly larger averages, possibly due to more available land.
Smaller homes: Coastal and densely populated states (e.g., New York, California) tend to have smaller average house sizes.
Price Range by US State
Code
map_extremes <- data |>group_by(state) |>summarise(min_price =suppressWarnings(min(price, na.rm =TRUE)),max_price =suppressWarnings(max(price, na.rm =TRUE)),.groups ="drop" ) |>mutate(range_price = max_price - min_price) |>inner_join(valid_states, by =c("state"="state_name"))plot_ly( map_extremes,type ="choropleth",locationmode ="USA-states",locations =~state_abbr,z =~range_price,text =~paste0( state,"<br>Min: $", formatC(min_price, big.mark =",", format ="f", digits =0),"<br>Max: $", formatC(max_price, big.mark =",", format ="f", digits =0) ),colorscale ="Reds",colorbar =list(title ="Price Range ($)")) |> plotly::layout(title =list(text ="Price Extrem Values by U.S. State (Max − Min)"),geo =list(scope ="usa", projection =list(type ="albers usa")) )
Interpretation
Highest ranges: California shows by far the largest price range (over $400M), driven by extremely high luxury property values.
Moderate ranges: States like Florida and parts of the Northeast also show wide price spreads, reflecting diverse markets from affordable to luxury homes.
Lower ranges: Most central and midwestern states have smaller price gaps, indicating more uniform housing markets.
Summary
Source Code
---title: "Data Exploration Gabriel Hamulic"subtitle: "Dataset: US Real Estate Dataset"author: "Hamulic, Gabriel"date: todayembed-resources: trueformat: html: output-file: US-Real-Estate_Gabriel_Hamulic.html #output-ext: "html.html" toc: true toc-location: right code-link: true code-tools: true #df-print: kable theme: light: flatly dark: darkly #echo: fenced pdf: output-file: US-Real-Estate_Gabriel_Hamulic.pdf toc: true number-sections: true code-link: true df-print: tibble crossref: lof-title: "List of Figures"fig-align: centerexecute: warning: false---\listoffigures \listoftables\listoflistings::: callout-caution### InstructionsYour report must be of high quality, meaning that your report:- is visually and textually pleasing of- does not look/read/feel like a draft instead of a finished analysis- explains/discusses your findings and results in the main text, e.g., explain/discuss all figures/table in the main text- is representable such that it can show to any interested third party- uses figure/table captions/linking/reference (see example further down)- Do not show any standard printout of R-code, use for data.frame/tibbles `knitr::kable()` printing.- Do not simply print datasets (too many lines) use instead `rmarkdown::paged_table()`:::{{< pagebreak >}}# Introduction## Libraries```{r}#| code-summary: Libraries#| code-fold: truelibrary <-function(...) {suppressPackageStartupMessages(base::library(...))}library(tidyverse)library(dplyr)library(knitr)library(tidyr)library(rmarkdown)library(janitor)library(scales)library(tidytext)library(ggforce)library(GGally)library(DT)library(kableExtra)library(broom)library(plotly)```# Data## Data sourceIn this data exploration we are looking at the US Real Estate market with use of a dataset from kaggle published by Ahmed Shahriar Sakib. It contains over 2.2 Million Real Estate listings broken down to State, Size, Price (among other factors). (Source: <https://www.kaggle.com/datasets/ahmedshahriarsakib/usa-real-estate-dataset/data>)## Data import```{r setup, include=FALSE}options(dplyr.print_max = 15, dplyr.print_min = 10)``````{r}data =read.csv("data/realtor-data.zip.csv") # Data import```## Data Transformation```{r}data =subset(data, select =c(status, price, bed, bath, acre_lot, city, state, house_size)) # keep relevant columns```### Structure with standard datatypes```{r}#| label: "data_structure"#| tbl-cap: "Structure of cleaned dataset"#| code-fold: truestructure_tbl <- tibble::tibble(Variable =names(data),Type =sapply(data, function(x) class(x)[1]),Example =sapply(data, function(x) { val <-unique(x[!is.na(x)])[1]if (is.factor(val)) as.character(val) }),Missing =sapply(data, function(x) sum(is.na(x))))kable( structure_tbl,caption ="Structure summary of the dataset",align =c("l", "l", "l", "r"))``````{r}#| code-fold: true# Assign Data Typesdata$status =as.factor(data$status)data$city =as.factor(data$city)data$state =as.factor(data$state)```### NA Removal```{r}#| code-fold: truebefore_rows <-nrow(data)data <-na.omit(data)after_rows <-nrow(data)kable(data.frame(Description =c("Before NA removal", "After NA removal"),Rows =c(before_rows, after_rows)))```The dataset now has `r nrow(data)` observations and `r ncol(data)` variables after removing rows with missing values.### Filtering```{r}#| code-fold: true# Filter min and max valuesdata = data |>filter(price >10000& price <1000000000)```### Calculations```{r}#| code-fold: truedata = data |>mutate(price_per_sqm = price/house_size)```### Cleaned Dataset```{r}#| code-fold: truepaged_table(data)```### Structure after transformation```{r}#| label: "data_structure_after_transformation"#| tbl-cap: "Structure of cleaned dataset"#| code-fold: truestructure_tbl <- tibble::tibble(Variable =names(data),Type =sapply(data, function(x) class(x)[1]),Example =sapply(data, function(x) { val <-unique(x[!is.na(x)])[1]if (is.factor(val)) as.character(val) elseas.character(round(val, 2)) }),Missing =sapply(data, function(x) sum(is.na(x))))kable( structure_tbl,caption ="Structure summary of the dataset",align =c("l", "l", "l", "r"))```After cleaning the dataset, all variables have appropriate data types and no missing values (n = `r nrow(data)`):- status – Factor variable showing the listing status (e.g., for_sale, sold).- price – Numeric value for the property’s price in USD.- bed, bath – Integer counts of bedrooms and bathrooms.- acre_lot – Numeric size of the lot (in acres).- city, state – Factor variables identifying the property’s location.- house_size – Numeric size of the house (in square feet).- price_per_sqm – Numeric variable derived from price / house_size to compare prices across properties.All rows with missing data were removed, and categorical variables were converted to factors for easier analysis and visualization later on.## Data dictionary```{r}#| code-fold: truetibble(Variable =c("price", "status", "acre_lot", "state", "house_size"),Description =c("The price for which the item was listed on the market","The status if the house is already sold or still for sale","The size of the land / lot on which the house is located in acres","The state in which the house is located","The size of the house in square feet" )) |>kable(caption ="Description of key variables in the dataset",align =c("l", "l") )```# Summary statistic tablesIn this section we will cover the summary of our cleaned dataset. We will explore basic statistical values from our data.## Numeric Statistics### Summary of numerical values```{r}#| label: "Numeric Statistics"#| tbl-cap: "Summary statistics of numerical variables in dataframe"#| code-fold: truedata |> janitor::clean_names() |>mutate(row =row_number() |>factor()) |>pivot_longer(cols =where(is.numeric)) |>group_by(name) |>summarize(N =n(),min =min(value),mean =mean(value),median =median(value),max =max(value),st.dev =sd(value) ) |> knitr::kable(digits =2)```#### Interpretation**price**: Very wide range (\$10.4k–\$51.5M). Mean (\$573k), median (\$379k), indicating strong right-skew and high-priced outliers.**house_size**: Average ~2,119 sqft, median 1,812 sqft. Extremely large max (1,560,780 sqft) signals outliers. The distribution is right-skewed.**acre_lot**: Median 0.21 acres vs. mean 12.75 acres → a few very large parcels inflate the mean.**bed / bath**: Typical homes (~3 beds, 2 baths) with modest spread; minima at 1 suggest realistic counts.**price_per_sqm**: Mean \$262.42 vs. median \$197.42, also right-skewed, consistent with price outliers.### Visualisation of numerical values```{r}#| label: "Logarithmic Visualisation"#| tbl-cap: "Visualisation of numerical variables in dataframe"#| code-fold: truedata |>clean_names() |>pivot_longer(cols =where(is.numeric)) |>ggplot(aes(x = value, fill = name)) +geom_histogram(bins =30, alpha =0.7, color ="white") +scale_x_log10(labels =label_comma()) +# 👈 echte Werte, log-Skalafacet_wrap(~ name, scales ="free_x") +theme_minimal() +labs(title ="Distribution of Numerical Variables (logarithmic scale)",x ="Value",y ="Count" ) +theme(legend.position ="none",axis.text.x =element_text(angle =25, hjust =1) )```## Nominal Statistics### Summary of nominal variables (top categories)```{r}#| label: "Nominal Statistics"#| tbl-cap: "Top categories for factor variables with counts, proportions, and mean price"#| code-fold: truetop_n_per_var <-10nominal_summary <- data |>clean_names() |>select(where(is.factor), price) |>pivot_longer(cols =where(is.factor),names_to ="Variable",values_to ="Category") |>group_by(Variable, Category) |>summarise(Count =n(),Percent =round(100* Count /nrow(data), 2),Mean_Price =round(mean(price, na.rm =TRUE), 0),.groups ="drop" ) |>group_by(Variable) |>slice_max(order_by = Count, n = top_n_per_var, with_ties =FALSE) |>ungroup()kable( nominal_summary,caption =paste0("Top ", top_n_per_var," categories per factor variable (counts, share %, and mean price)" ),digits =2,align =c("l", "l", "r", "r", "r"))```#### Interpretation**city**: Most listings in Houston, Tucson, Phoenix, and Los Angeles. Prices range widely — highest in Los Angeles (~\$1.9M), lowest around \$250k (Saint Louis).**state**: California, Texas, and Florida dominate listings (>30% total). California shows the highest mean price (~\$1.1M).**status**: 55% for sale, 45% sold. Active listings are priced higher (~\$621k vs. \$515k).**Overall**: Listings cluster in major U.S. cities and states, with strong regional price differences, especially high in California and large metro areas.### Visualisation of nominal variables (top categories)```{r}#| label: "Visualization Nominal Statistics"#| tbl-cap: "Top categories for factor variables with counts, proportions, and mean price"#| code-fold: truenominal_summary <- nominal_summary |>group_by(Variable) |>mutate(Category = forcats::fct_reorder(Category, Count),Category =factor(Category, levels =unique(Category))) |>ungroup()# Plot: Facets untereinander, mit eigener x-Skala und y-Skala pro Variableggplot(nominal_summary, aes(x = Count, y = Category, fill = Variable)) +geom_col(show.legend =FALSE, alpha =0.8, width =0.7) +facet_wrap(~ Variable, ncol =1, scales ="free", drop =TRUE) +scale_x_continuous(labels =label_comma()) +#Tausendertrennung, keine 1e+05theme_minimal() +labs(title ="Top Categories per Factor Variable",x ="Count",y ="Category" ) +theme(panel.spacing.y =unit(1, "lines"),strip.text =element_text(size =12, face ="bold"),axis.text.y =element_text(size =8),plot.margin =margin(5, 15, 5, 5) )```# Bivariate Analysis### Pairs Plot (all numeric variables)```{r}#| label: "Pairs Plot"#| code-fold: trueset.seed(123)data_num <- data |> janitor::clean_names() |>select(where(is.numeric)) |>slice_sample(n =3000) |>mutate(across(everything(), log1p)) p <-ggpairs( data_num,progress =FALSE,upper =list(continuous =wrap("cor", size =4, alignPercent =0.8, stars =TRUE)),lower =list(continuous =wrap("points", alpha =0.3, size =0.7)),diag =list(continuous =wrap("densityDiag", alpha =0.7)))p +theme_minimal(base_size =11) +theme(strip.text =element_text(size =8, face ="bold"),panel.grid =element_blank(),axis.text =element_text(size =8),axis.title =element_text(size =9),plot.title =element_text(face ="bold", size =14, hjust =0.5) ) +labs(title ="Scatterplot-Matrix (log-transformiert, n=3000)")```### Price vs. House Size by Status```{r}#| label: "scatter_price_size"#| tbl-cap: "Price vs. house size by listing status"#| code-fold: true# Stichprobe ziehen für Performanceset.seed(123)sample_data <- data %>%sample_n(50000)plot_ly( sample_data,x =~house_size,y =~price,color =~status,type ="scatter",mode ="markers",alpha =0.6) %>% plotly::layout(title =list(text ="Relationship Between House Size and Price by Status"),xaxis =list(title ="House Size (sqft)"),yaxis =list(title ="Price ($)", type ="log") )```#### Interpretation **Positive relationship**: Larger houses generally have **higher prices**, though the relationship weakens for very large properties.**Status comparison**: Both for_sale and sold homes follow **similar trends**, but **for_sale** listings appear higher in price, suggesting sellers may list above sale values.**High variation**: At similar sizes, prices vary widely — showing the strong influence of **location** and other factors.**Outliers**: A few extremely large or expensive properties stretch the scale upward.### Multiple Regression```{r}#| code-fold: truemodel <-lm(price ~ house_size + bath + bed + state + status, data = data)tidy(model) |>arrange(p.value) |>mutate(estimate =round(estimate, 1),std.error =round(std.error, 1),statistic =round(statistic, 1),p.value =signif(p.value, 3) ) |>datatable(caption ="Regressionsergebnisse (interaktiv)",filter ="top", options =list(pageLength =10, autoWidth =TRUE,responsive =TRUE ) )``````{r}#| label: "Graphic Regression"#| code-fold: truetidy(model, conf.int =TRUE) |>filter(term !="(Intercept)") |>mutate(term =reorder(term, estimate)) |>ggplot(aes(x = estimate, y = term, fill = estimate >0)) +geom_col(show.legend =FALSE) +geom_vline(xintercept =0, linetype ="dashed") +theme_minimal() +labs(title ="Greatest contributors to price",x ="regression coefficient",y ="" )```### Average Property Price Map```{r}#| label: "state_mapping"#| code-fold: truevalid_states <-tibble(state_name =c(state.name, "District of Columbia"),state_abbr =c(state.abb, "DC"))``````{r}#| label: "map_avg_price"#| tbl-cap: "Average property price by U.S. state"#| code-fold: truemap_price <- data |>group_by(state) %>%summarise(avg_price =mean(price, na.rm =TRUE), .groups ="drop") |>inner_join(valid_states, by =c("state"="state_name")) |>mutate(avg_price_k = avg_price /1000)plot_ly( map_price,type ="choropleth",locationmode ="USA-states",locations =~state_abbr,z =~avg_price_k,text =~paste0(state, "<br>Avg Price: $", round(avg_price_k, 1), "K"),colorscale ="Blues",colorbar =list(title ="Avg Price ($K)")) |> plotly::layout(title =list(text ="Average Property Price by U.S. State"),geo =list(scope ="usa", projection =list(type ="albers usa")) )```#### Interpretation **Regional variation**: Western and coastal states show generally **higher property prices**, while central regions are lower.**Highest averages**: States like **California, New York, and Washington** stand out with mean prices well above **$1M**.**Moderate prices**: States such as Texas, Florida, and Arizona fall in the **mid-range** (~$400–650K).**Lower averages**: Midwest and Southern states have more affordable properties on average.**Summary**: Property values are heavily influenced by **geography** — with the highest prices concentrated along the coasts and major urban centers.### Average House Size Map```{r}#| label: "map_avg_size"#| tbl-cap: "Average house size by U.S. state"#| code-fold: truemap_size <- data %>%group_by(state) %>%summarise(avg_size =mean(house_size, na.rm =TRUE), .groups ="drop") %>%inner_join(valid_states, by =c("state"="state_name"))plot_ly( map_size,type ="choropleth",locationmode ="USA-states",locations =~state_abbr,z =~avg_size,text =~paste0(state, "<br>Avg Size: ", round(avg_size), " sqft"),colorscale ="Greens",colorbar =list(title ="Avg Size (sqft)")) %>% plotly::layout(title =list(text ="Average House Size by U.S. State"),geo =list(scope ="usa", projection =list(type ="albers usa")) )```#### Interpretation **General trend**: Average house sizes are fairly consistent across most states, typically around 2,000–2,500 sqft.**Larger homes**: Some central and mountain states (e.g., Colorado, Utah, Iowa) show slightly larger averages, possibly due to more available land.**Smaller homes**: Coastal and densely populated states (e.g., New York, California) tend to have smaller average house sizes.### Price Range by US State```{r}#| label: "map_extreme_price"#| tbl-cap: "Price range (max − min) by U.S. state"#| code-fold: truemap_extremes <- data |>group_by(state) |>summarise(min_price =suppressWarnings(min(price, na.rm =TRUE)),max_price =suppressWarnings(max(price, na.rm =TRUE)),.groups ="drop" ) |>mutate(range_price = max_price - min_price) |>inner_join(valid_states, by =c("state"="state_name"))plot_ly( map_extremes,type ="choropleth",locationmode ="USA-states",locations =~state_abbr,z =~range_price,text =~paste0( state,"<br>Min: $", formatC(min_price, big.mark =",", format ="f", digits =0),"<br>Max: $", formatC(max_price, big.mark =",", format ="f", digits =0) ),colorscale ="Reds",colorbar =list(title ="Price Range ($)")) |> plotly::layout(title =list(text ="Price Extrem Values by U.S. State (Max − Min)"),geo =list(scope ="usa", projection =list(type ="albers usa")) )```#### Interpretation **Highest ranges**: California shows by far the **largest price range** (over $400M), driven by extremely high luxury property values.**Moderate ranges**: States like Florida and parts of the Northeast also show wide **price spreads**, reflecting diverse markets from affordable to luxury homes.**Lower ranges**: Most central and midwestern states have smaller price gaps, indicating more uniform housing markets.# Summary